# What exactly is centrifugal force

by hms.tech
Tags: centrifugal, force
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Just throwing in my 2 cents worth.
 Quote by A.T. That is why I prefer the terms "inertial forces" and "interaction forces".
I agree with A.T. here. Fictitious forces do most things that you expect real forces to do, including do work in the non-inertial frame in which they exist.
 Quote by Andrew Mason The true reaction to a centripetal force is another centripetal force.
This can be true in certain circumstances, but it is not generally true.
 Quote by stevendaryl So some people would take this to mean "Newton's laws only apply in an inertial frame". I don't like that conclusion. If you view them as vector equations, then they apply in all circumstances, not just inertial frames.
Interesting idea. I was aware of this in terms of gravity in GR, but hadn't thought clearly about the advantage for Newtonian physics also. As we discussed in that other thread, I am not convinced about this because of the double-degeneracy of the metric in Newtonian physics. But I haven't looked at it closely (for that same reason).
 Quote by Andrew Mason There is nothing about the "centrifugal reaction force" that causes anything to flee from the centre. Nothing.
This is simply wrong. If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.
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 Quote by Andrew Mason Suppose we have two spherical moons orbiting a spherical planet and both moons are directly opposite each other (ie. a line through the moons' centres passes through the planet's centre) on identical orbits. Would you say that that the reaction forces of each moon on the planet are centrifugal?
In this situation, there is no reaction force, because there is nothing to exert a reaction force onto. The only forces are gravitational. The only "outwards" force would be exerted onto the surface of the planet, but that force is due to gravity, not a reaction force. In this situation, the reaction to gravitational force is a change in the path of the moons as they orbit.

 Quote by DaleSpam If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.
A reactive force is a response to acceleration of an object wrt inertial frame. In an inertial frame, once the floor is cut, the astronaut and the floor cease to accelerate, so there is no reactive centrifugal force. In a rotating frame, the reactive centrifugal force also vanishes (the astronaut ceases to exert a force onto the floor), and the fictitious centrifugal force now changes in to a combination of fictitious centrifugal and coriolis forces that correspond to an object moving at constant velocity wrt inertial frame, as observed from a rotating frame.
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 Quote by A.T. Then I'm sure you will soon have convinced anyone to stop using them. Let us know when all the books have been revised.
There are lots of bad ideas that are taught to beginning students of physics that have to be "untaught" to advanced students. Inertial forces is one of them. "Relativistic mass" is another.

 It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.
It doesn't lead to ANYTHING. Calling something a "force" when it's not is just bad terminology. It's not an alternative approach to doing physics.
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 Quote by sophiecentaur This thread reads like something out of Gulliver's Travels, actually. Anyone would think that there is some actual 'reality' in it all. People don't acknowledge that Science is the pragmatic business of predicting things - all the rest is faith.
The claim that "Science is the pragmatic business of predicting things - all the rest is faith" is itself a philosophical position, and is therefore, not science.
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 Quote by stevendaryl It doesn't lead to ANYTHING.
It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.
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 Quote by A.T. It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.
Calling something a "force" doesn't lead to ANYTHING. If you think otherwise, give an example of how something follows from the fact that you call certain terms "forces".
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 Quote by A.T. It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.
The claim that nothing matters other than quantitative predictions is itself a philosophical claim. It's funny that the people who bring up "that's just philosophy" as an argument are the ones who actually end up making the strongest philosophical claims.
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 Quote by stevendaryl The claim that nothing matters other than quantitative predictions...
...in physics.
 Quote by stevendaryl It's funny that the people who bring up "that's just philosophy" as an argument...
The argument is "The rest is philosophy, so there is no point arguing about it on a physics forum".
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 Quote by A.T. The argument is "The rest is philosophy, so there is no point arguing about it on a physics forum".
But that's basically this entire thread. The physics part is nothing more than:

"If one uses noninertial, curvilinear coordinates, then additional terms appear in the equations of motion."

One sentence. Everything else is an argument for a particular way of looking at those additional terms.
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 Quote by stevendaryl give an example of how something follows from the fact that you call certain terms "forces".
All forces are just "certain terms". So I don't see how this is an argument against inertial forces specifically.
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 Quote by A.T. It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.
I also want to point out that connection coefficients (the preferred, in my opinion, way to deal with noninertial, curvilinear coordinates) are essential to understanding General Relativity.
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 Quote by A.T. All forces are just "certain terms". So I don't see how this is an argument against inertial forces specifically.
No, they're not. Real forces have certain properties that the fake forces don't:
(1) They are vector quantities, meaning that they exist in EVERY coordinate system. The components change when you change coordinate systems, but a vector is a geometric quantity that is independent of coordinates.
(2) Real forces have corresponding reaction forces, leading to conservation of momentum.

In contrast, "inertial forces" are artifacts of a particular choice of coordinates. They don't have corresponding reaction forces. They can be made to disappear by choosing the appropriate coordinate system.
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 Quote by rcgldr In a rotating frame, the reactive centrifugal force also vanishes (the astronaut ceases to exert a force onto the floor),
You can easily find examples where reactive centrifugal force pushes things outwards in the rotating frame. Two blocks on a turntable. An outer light one with high friction. An inner massive one on rollers. The inner block applies a centrifugal interaction force to the outer block, which pushes the outer block away from the center in the rotating frame.

But all of that is not relevant to the "centrifugal"-label for the reason I state in post #64.
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 Quote by stevendaryl Real forces have certain properties...
Give an example of how something follows from the fact that you call them "forces".
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 Quote by stevendaryl The claim that "Science is the pragmatic business of predicting things - all the rest is faith" is itself a philosophical position, and is therefore, not science.
Haha
I suppose I have to take your point because my suggestion is not falsifiable. But I think that the inverse, - i.e. that Science definitely can establish 'real truth'- probably is falsifiable. So far, we have found this as our experience has been that Science, and its models, continuously changes to fit new evidence.
It has to be true that Science endeavors to avoid saying what things 'really are' because there are so many examples of two or more, equally valid 'realities'. (Note, I write "Science" and not 'Scientists' - who are human and fallible and seldom view things without the distraction of some sort of faith).
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 Quote by DaleSpam This is simply wrong. If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.
I have to strongly disagree. It is not reactive centrifugal force that will cause the section to move farther away from the centre. It is the fictitious centrifugal force that would cause that (ie. it is inertia - the absence of centripetal force). The reactive centrifugal force disappears immediately as soon as the bolts are cut. This is exactly why the term "reactive centrifugal force" should not be used. It gets confused with the fictitious centrifugal force.

AM
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 Quote by Andrew Mason I have to strongly disagree. It is not reactive centrifugal force that will cause the section to move farther away from the centre. It is the fictitious centrifugal force that would cause that (ie. it is inertia - the absence of centripetal force). The reactive centrifugal force disappears immediately as soon as the bolts are cut. This is exactly why the term "reactive centrifugal force" should not be used. It gets confused with the fictitious centrifugal force. AM
But the other astronaut (sitting in the frame of the wheel) will see the departing astronaut accelerating, initially (during the first 90 degrees of motion, at least) and due to the geometry of the situation. Would he not conclude that there is a force still operating? This perceived force will also be making the departed astronaut perform a spiral outward path - so it would (might) not just be a centrifugal force that he would need in order to explain the guy's path.
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 Quote by A.T. Give an example of how something follows from the fact that you call them "forces".
Of course, it doesn't matter what you call them, but the point is that Newton's laws relate motion of one object to vector quantities produced by other objects:

$m \frac{\stackrel{\rightarrow}{dU}}{dt} = \stackrel{\rightarrow}{F}$

The left-hand side is a fact about the motion of the object, and the right-hand side is about the external situation affecting that motion. In terms of coordinates:

$(\frac{\stackrel{\rightarrow}{dU}}{dt})^i = \frac{dU^i}{dt} +$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k$

where $\Gamma^i_{jk}$ are the so-called "connection coefficients", which are due to using nonconstant basis vectors. So the full equations of motion, in terms of components, are:

$m(\frac{dU^i}{dt} +$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k) = F^i$

What the idea of "fictitious forces" amounts to is moving the extra terms from the left side (where they describe motion) to the right side (where they are treated as forces):

$m \frac{dU^i}{dt} = F^i + F_{inertial}^i$

where
$F_{inertial}^i = - m$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k$

What difference does it make whether you group it on the left side, or the right side? Well, for one thing, when it comes to figuring out the reaction forces (Newton's third law), only the $F^i$ term is relevant. There are no reaction forces to $F_{inertial}^i$. For another, since real forces are vectors, the components transform in a standard way under a coordinate change: If you change coordinates from $x^i$ to $y^b$, then

$F^b =$ sum over $i$ of $\dfrac{\partial y^b}{\partial x^i} F^i$

"Inertial forces" DON'T transform that way.

So sure, you can group whatever terms together you want, and call them whatever you want to call them, but when it comes to reasoning about the physics, you have to separate out the "real" forces from the "inertial" forces. You're basically doing extra steps that have to be undone later.

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